Friday, September 15, 2006

Which is the most remarkable and under-appreciated paper about QFT?

Take a look at this paper:

Hideji Kita, A Non-Trivial Example of a Relativistic Quantum Theory of Particles without Divergence Difficulties Prog. Theor. Phys. 35 (1965) 934.

Kita builds a fully relativistic theory of interacting particles without even mentioning quantum fields. This theory doesn't have self-interactions and doesn't require renormalization. Both the Hamiltonian and the boost operator are constructed explicitly. They can be used to calculate the time evolution and boost (Lorentz) transformations of observables to the moving reference frame.

He also translates his theory in the language of quantum fields and explicitly shows how the Haag's theorem works. The "interacting quantum field" does not transform covariantly under boost transformations. (Who cares?)

Unfortunately, this work didn't have any impact on the development of QFT. Now it seems to be completely forgotten.

Kita also had a few follow-up papers in Prog. Theor. Phys. in 1960's and 70's. They are real treats!


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